98 ANALYTICAL MECHANICS acceleration. Therefore the unit is the ^~?2. The dimen- oC'C'* sions of angular acceleration are given by [T~2]. ILLUSTRATIVE EXAMPLE. A particle moves so that the coordinates of its position at any instant are given by the equations x — a cos kt, y = a sin kt. Find the acceleration and its components. In a previous illustrative example, p. 82, it was shown that these equations represent uniform circular motion, with the following data: v = ka, co = kj vx = — ka sin kt, vr = 0, vy — ka cos kt, vp = ka. Therefore , — — K X) dt = — k~ a sin kt f _ 1 d / = - Fa, w = -k = 0, = - to2. W6 It will be observed that fr has a value different from zero, while vr is nil. PROBLEMS. 1. A flywheel making 250 revolutions per minute is brought to rest in 2 minutes. Find the average angular acceleration. 2. A flywheel making 250 revolutions per minute is retarded by a constant acceleration of — 5 -^~- . How many revolutions will the flv- sec.2 J wheel make before stopping? 3. In the preceding problem find the time it takes the flywheel to 3ome to rest. 4. Find the angular velocity and angular acceleration of a particle moves in a manner defined by the following pairs of equations : (a) p = a sin cotf, 6 — b sin cat. (b) p = a sin cot, 6 = 1} cos coZ. (c) p = a sin co£, 6 = bt. (d) p = ae**, o = bt. 5. In problem 4 find the equation of the path and plot it.